Problem Statement:
- Consider a village with demons and a sleeping man(who never wakes up).
- Note that a demon can eat the sleeping man, but after eating him, the demon falls asleep.
- Similarly, any demon can eat any other sleeping demon, and this process repeats.
- Assume that the demons are very smart and would always choose to stay alive than to eat the man and risk their lives.
- Initially, there are 65 demons and 1 sleeping man. What would happen in the village?
Solution:
Below given are few simpler cases for a better understanding of the above-given problem statement:
Case 1: 1 Demon and a sleeping man
In this case, the demon will eat the sleeping man. As demon knows, there is no one to eat him.
Case 2: 2 Demon and a sleeping man
- Nothing will happen in this case.
- If any of the demons eat the sleeping man, then the demon knows that the remaining demon will kill him.
- So both the demons would decide not to eat the sleeping man.
Case 3: 3 Demon and a sleeping man
- In this case, one of the demons would eat the sleeping man.
- As demon knows that the remaining 2 demons would choose not to eat him.
- As it would make them unsafe(consider case 2).
Case 4: 4 Demons and a sleeping man
- In this case, nothing will happen.
- All the demons will choose not to eat the sleeping man as they know that any of the remaining 3 demons would eat him.
Conclusion:
- From the above 4 cases, it can be concluded that, if there are an odd number of eaters and one sleeping target(be it man or demon). The demon will decide to eat the target.
- If there are even several eaters then nothing will happen because if the demon eats the target then he would become the target.
- In the given problem, there are 65 demons(odd number of eaters). Therefore, one demon eats the sleeping man and nothing happens thereafter.
Another way to understand:
Since an even number can be divided in pairs of 2, so if the number of demons are even, then no demon would risk to eat the sleeping target as he knows he would become the target.
But if the number of demons are odd, then one of the demons would eat the sleeping target because he knows that thereafter no one would eat him as the number of demons remaining would be even (so they would be in pairs and they would know that if they eat the sleeping target, then they would become a target themselves).